Parallel solution of three-dimensional Marangoni flow in liquid bridges

This paper describes the implementation and performances of a parallel solver for the direct numerical simulation of the three-dimensional and time-dependent Navier-Stokes equations on distributed-memory, massively parallel computers. The feasibility of this approach to study Marangoni flow instability in half zone liquid bridges is examined. The results indicate that the incompressible, non-linear Navier-Stokes problem, governing the Marangoni flows behavior, can effectively be parallelized on a distributed memory parallel machine by remapping the distributed data structure. The numerical code is based on a three-dimensional Simplified Marker and Cell (SMAC) primitive variable method applied to a staggered finite difference grid. Using this method, the problem is split into two problems, one parabolic and the other elliptic A parallel algorithm, explicit in time, is utilized to solve the parabolic equations. A parallel multisplitting kernel is introduced for the solution of the pseudo pressure elliptic equation, representing the most time-consuming part of the algorithm. A grid-partition strategy is used in the parallel implementations of both the parabolic equations and the multisplitting elliptic kernel. A Message Passing Interface (MPI) is coded for the boundary conditions; this protocol is portable to different systems supporting this interface for interprocessor communications. Numerical experiments illustrate good numerical properties and parallel efficiency. In particular, good scalability on a large number of processors can be achieved as long as the granularity of the parallel application is not too small. However, increasing the number of processors, the Speed-Up is ever smaller than the ideal linear Speed-Up. The communication timings indicate that complex practical calculations, such as the solutions of the Navier-Stokes equations for the numerical simulation of the instability of Marangoni flows, can be expected to run on a massively parallel machine with good efficiency. Copyright (C) 1999 John Wiley & Sons, Ltd.